Tìm x biết x-1/2019+x-2/2018=x-3/2017+x-4/2016 CẢM ƠN Ạ
2 câu trả lời
Đáp án: $x=2020$.
Giải thích các bước giải:
`{x-1}/2019 + {x-2}/2018 = {x-3}/2017 + {x-4}/2016`
`⇔ {x-1}/2019 + {x-2}/2018 -2= {x-3}/2017 + {x-4}/2016 -2`
`⇔ ({x-1}/2019 -1) + ({x-2}/2018 -1)= ({x-3}/2017 -1) + ({x-4}/2016 -1)`
`⇔ {x-2020}/2019 + {x-2020}/2018 = {x-2020}/2017 + {x-2020}/2016`
`⇔ {x-2020}/2019 + {x-2020}/2018 - {x-2020}/2017 - {x-2020}/2016 =0`
`⇔ (x-2020).(1/2019 + 1/2018 - 1/2017 - 1/2016)=0`
`⇔ x=2020` (`1/2019 + 1/2018 - 1/2017 - 1/2016 \ne 0`)
Vậy `x=2020`.
Đáp án:
`x=2020`
Giải thích các bước giải:
`(x-1)/2019+(x-2)/2018=(x-3)/2017+(x-4)/2016`
`⇔((x-1)/2019-1)+((x-2)/2018-1)=((x-3)/2017-1)+((x-4)/2016-1)`
`⇔(x-1-2019)/2019+(x-2-2018)/2018=(x-3-2017)/2017+(x-4-2016)/2016`
`⇔(x-2020)/2019+(x-2020)/2018=(x-2020)/2017+(x-2020)/2016`
`⇔(x-2020)/2019+(x-2020)/2018-(x-2020)/2017-(x-2020)/2016=0`
`⇔(x-2020)(1/2019+1/2018-1/2017-1/2016)=0`
`⇔x-2020=0` (vì `1/2019+1/2018-1/2017-1/2016\ne0`)
`⇔x=2020`
Vậy `x=2020`